An adjoint state method for three-dimensional transmission traveltime tomography using first-arrivals. (English) Zbl 1096.65062

Leung, Shingyu; Qian, Jianliang

Commun. Math. Sci. 4, No. 1, 249-266 (2006).

Summary: Traditional transmission travel-time tomography hinges on ray tracing techniques. We propose a partial differential equation based Eulerian approach to travel-time tomography so that we can avoid using the cumbersome ray-tracing technique. We start from the eikonal equation, define a mismatching functional and derive the gradient of the nonlinear functional by an adjoint state method. The resulting forward and adjoint problems can be efficiently solved by using the fast sweeping method; a limited memory Broyden-Fletcher-Goldfarb-Shanno method is used to drive the mismatching functional to zero with quadratic convergence. 2D and 3D numerical results as well as Marmousi synthetic velocity model demonstrate the robustness and the accuracy of the method.

MSC:

65K10	Numerical optimization and variational techniques
49J20	Existence theories for optimal control problems involving partial differential equations
49M15	Newton-type methods
86A22	Inverse problems in geophysics
49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games

Keywords:

seismics; viscosity solution; fast sweeping method; numerical examples; inverse problem; ray tracing; travel-time tomography; eikonal equation; fast sweeping; Broyden-Fletcher-Goldfarb-Shanno method; quadratic convergence; numerical results